Math Problem Statement

7,20,47,94

Solution

The given sequence is: 7, 20, 47, 94.

To find the next term or a pattern in this sequence, let's first analyze the differences between consecutive terms:

  1. 207=1320 - 7 = 13
  2. 4720=2747 - 20 = 27
  3. 9447=4794 - 47 = 47

We observe that the differences are increasing in a specific pattern. Let's examine the differences between these differences:

  1. 2713=1427 - 13 = 14
  2. 4727=2047 - 27 = 20

So, the differences themselves are increasing by 6 each time (14, 20,...). If this pattern continues, the next difference should be:

47+(20+6)=47+26=7347 + (20 + 6) = 47 + 26 = 73

Therefore, the next term in the sequence is:

94+73=16794 + 73 = 167

The next term in the sequence is 167.

Would you like a detailed explanation or further analysis on this sequence?


Here are some related questions you might consider:

  1. Can we derive a general formula for this sequence?
  2. What kind of sequence is this (e.g., arithmetic, quadratic)?
  3. How does finding second differences help identify patterns in sequences?
  4. What is the importance of higher-order differences in sequence analysis?
  5. Can this pattern be modeled by a polynomial equation?

Tip: When analyzing number sequences, checking differences and second differences often helps detect hidden patterns.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Higher-Order Differences

Formulas

Difference of Consecutive Terms Formula
Higher-Order Difference Pattern

Theorems

Sequence Difference Theorem

Suitable Grade Level

Grades 7-10